Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body Systems

Abstract

We introduce a variational wavefunction for many-body ground states that involves imaginary time evolution with two different Hamiltonians in an alternating fashion with variable time intervals. We successfully apply the ansatz on the one- and two-dimensional transverse-field Ising model and systematically study its scaling for the one-dimensional model at criticality. We find the total imaginary time required scales logarithmically with system size, in contrast to the linear scaling in conventional Quantum Monte Carlo. We suggest this is due to unique dynamics permitted by alternating imaginary time evolution, including the exponential growth of bipartite entanglement. For generic models, the superior scaling of our ansatz potentially mitigates the negative sign problem at the expense of having to optimize variational parameters.